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Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 41CR: For T:P4R5, and rank (T)=3, find nullity (T).

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(d) Calculate the conditional probability P(X > 2 log 2|Y = log 2), where always log stands for
the natural logarithm.
(e) Show that E(E(X|Y)) = E(X).
(f) Calculate the m.g.f. Mx,y.

3. Let X and Y be two r.v.'s with joint p.d.f. given by:
fx,y(x, y) =
cye
e¯¤, 0 < y ≤ x <∞,
0, otherwise
(a) Determine the constant c.
(b) Determine the marginal p.d.f.'s fx and fy and specify the range of the arguments involved.
(c) Determine the conditional p.d.f.'s fxy (Ay) and fy|x(Ax), and specify the range of the
arguments involved.

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